Precalculus Examples

$\frac{\frac{s + 6}{s}}{\frac{4}{s}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{s + 6}{s} \cdot \frac{s}{4}$

Step 2

Cancel the common factor of $s$ .

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Step 2.1

Cancel the common factor.

$\frac{s + 6}{s} \cdot \frac{s}{4}$

Step 2.2

Rewrite the expression.

$(s + 6) \frac{1}{4}$

Step 3

Apply the distributive property.

$s \frac{1}{4} + 6 (\frac{1}{4})$

Step 4

Combine $s$ and $\frac{1}{4}$ .

$\frac{s}{4} + 6 (\frac{1}{4})$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $6$ .

$\frac{s}{4} + 2 (3) \frac{1}{4}$

Step 5.2

Factor $2$ out of $4$ .

$\frac{s}{4} + 2 \cdot 3 \frac{1}{2 \cdot 2}$

Step 5.3

Cancel the common factor.

$\frac{s}{4} + 2 \cdot 3 \frac{1}{2 \cdot 2}$

Step 5.4

Rewrite the expression.

$\frac{s}{4} + 3 (\frac{1}{2})$

Step 6

Combine $3$ and $\frac{1}{2}$ .

$\frac{s}{4} + \frac{3}{2}$

Step 7

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{s}{4} + \frac{3}{2} \cdot \frac{2}{2}$

Step 8

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{s}{4} + \frac{3 \cdot 2}{2 \cdot 2}$

Step 8.2

Multiply $2$ by $2$ .

$\frac{s}{4} + \frac{3 \cdot 2}{4}$

Step 9

Combine the numerators over the common denominator.

$\frac{s + 3 \cdot 2}{4}$

Step 10

Multiply $3$ by $2$ .

$\frac{s + 6}{4}$